Geometric Methods In The Algebraic Theory Of Quadratic Forms
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Geometric Methods In The Algebraic Theory Of Quadratic Forms
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Author : Oleg T. Izhboldin
language : en
Publisher: Springer
Release Date : 2004-02-07
Geometric Methods In The Algebraic Theory Of Quadratic Forms written by Oleg T. Izhboldin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-07 with Mathematics categories.
The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes an introduction to motives of quadrics by A. Vishik, with various applications, notably to the splitting patterns of quadratic forms, papers by O. Izhboldin and N. Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields with u-invariant 9, and a contribution in French by B. Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties.
Geometric Methods In The Algebraic Theory Of Quadratic Forms
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Author : Oleg T Tignol Jean-Pierre Izhboldin
language : en
Publisher: Springer
Release Date : 2014-01-15
Geometric Methods In The Algebraic Theory Of Quadratic Forms written by Oleg T Tignol Jean-Pierre Izhboldin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Geometric Methods In The Algebraic Theory Of Quadratic Forms
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Author :
language : en
Publisher:
Release Date : 2004
Geometric Methods In The Algebraic Theory Of Quadratic Forms written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Algebraic fields categories.
Geometric Methods In The Algebraic Theory Of Quadratic Forms
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Author : Oleg Tomovich Izhboldin
language : en
Publisher:
Release Date : 2004
Geometric Methods In The Algebraic Theory Of Quadratic Forms written by Oleg Tomovich Izhboldin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Geometric Methods In The Algebraic Theory Of Quadratic Forms
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2004
Geometric Methods In The Algebraic Theory Of Quadratic Forms written by and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Forms, Pfister categories.
The Algebraic And Geometric Theory Of Quadratic Forms
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Author : Richard S. Elman
language : en
Publisher: American Mathematical Soc.
Release Date : 2008-07-15
The Algebraic And Geometric Theory Of Quadratic Forms written by Richard S. Elman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-15 with Mathematics categories.
This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages of the development of the theory. Assuming only a basic course in algebraic geometry, Part II presents the necessary additional topics from algebraic geometry including the theory of Chow groups, Chow motives, and Steenrod operations. These topics are used in Part III to develop a modern geometric theory of quadratic forms.
Specialization Of Quadratic And Symmetric Bilinear Forms
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Author : Manfred Knebusch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-22
Specialization Of Quadratic And Symmetric Bilinear Forms written by Manfred Knebusch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-22 with Mathematics categories.
A Mathematician Said Who Can Quote Me a Theorem that’s True? For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick ?rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on ?eld invariants from the theory of quadratic forms. It is—poetic exaggeration allowed—a suitable motto for this monograph. What is it about? At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover ?elds[32].Let? : K? L?? be a place. Then one can assign a form? (?)toaform? over K in a meaningful way ? if? has “good reduction” with respect to? (see§1.1). The basic idea is to simply apply the place? to the coe?cients of?, which must therefore be in the valuation ring of?. The specialization theory of that time was satisfactory as long as the ?eld L, and therefore also K, had characteristic 2. It served me in the ?rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over ?elds, as can be seen from the book [26]of Izhboldin–Kahn–Karpenko–Vishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there).
Quadratic Forms Algebra Arithmetic And Geometry
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Author : Ricardo Baeza
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-08-14
Quadratic Forms Algebra Arithmetic And Geometry written by Ricardo Baeza and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-14 with Mathematics categories.
This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007. The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.
Algebraic Theory Of Quadratic Forms
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Author : Manfred Knebusch
language : en
Publisher: Birkhäuser
Release Date : 1980
Algebraic Theory Of Quadratic Forms written by Manfred Knebusch and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Juvenile Nonfiction categories.
Quadratic Forms And Their Applications
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Author : Eva Bayer-Fluckiger
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Quadratic Forms And Their Applications written by Eva Bayer-Fluckiger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This volume outlines the proceedings of the conference on "Quadratic Forms and Their Applications" held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.